How do you combine like terms in (5- x ) ( 5+ x ) + ( x - 5) ^ { 2} + ( 2x - 10) ( x + 3)(5−x)(5+x)+(x−5)2+(2x−10)(x+3)?

2 Answers
Lucy
Jul 27, 2018

2x^2-14x+202x2−14x+20

Explanation:

(5-x)(5+x)+(x-5)^2+(2x-10)(x+3)(5−x)(5+x)+(x−5)2+(2x−10)(x+3) can be separated into 3 parts:

  • (5-x)(5+x)=25-x^2(5−x)(5+x)=25−x2 (difference of 2 squares)

  • (x-5)^2=x^2-10x+25(x−5)2=x2−10x+25 (perfect squares)

  • (2x-10)(x+3)=2x^2-4x-30(2x−10)(x+3)=2x2−4x−30

(5-x)(5+x)+(x-5)^2+(2x-10)(x+3)(5−x)(5+x)+(x−5)2+(2x−10)(x+3)
=25-x^2+x^2-10x+25+2x^2-4x-30=25−x2+x2−10x+25+2x2−4x−30
=25cancel(-x^2+x^2)-10x+25+2x^2-4x-30
=2x^2-14x+20

Cem Sentin
Jul 27, 2018

2x^2-14x+20

Explanation:

(5-x)(5+x)+(x-5)^2+(2x-10)(x+3)

=25-x^2+x^2-10x+25+2x^2-4x-30

=2x^2-14x+20

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